Question

If t varies as v, and t = 2 4/7 when v =13/14 , find v when t = 2 1/4

a) 2106/392
b) 13/16
c) 324/52

Answer 1

Answer : b) 13/16

Given : t varies as v

So t = k v  where k is the constant of proportionality.

t = 2 4/7 when v =13/14. Using these values we find out k

$t = 2\frac{4}{7} =\frac{18}{7}$

$v =\frac{13}{14}$

t = k * v

$\frac{18}{7}= k *\frac{13}{14}$

Multiply by 14/13 on both sides

$\frac{18}{7} *\frac{14}{13} = k *\frac{13}{14}*\frac{14}{13}$

So  $k =\frac{36}{13}$

We got the value of k. Now we find v when t = 2 1/4

$t = 2\frac{1}{4} =\frac{9}{4}$

t = k * v

We know the value of t and k

$\frac{9}{4}= \frac{36}{13}* v$

Multiply by 13/36 on both sides

$\frac{9}{4} *\frac{13}{36} =\frac{36}{13}*\frac{13}{36}* v$

So  $\frac{13}{16}= v$

Option B is correct